Two methods used in artery deep cryopreservation, "Cryopreservation in Medium" and "Cryopreservation in Air", were studied. For the former method, samples were frozen together with a certain amount of cryoprotectants (CPA) in the cryovial or cryobag, while for the other method the arteries were first exposed to CPA and then frozen without the CPA medium surrounding in the cryovial. Study of the cryopreserved arteries using these two methods found that "cryopreservation in air" could substantially reduce the fracture rate of the arteries. To explain the difference theoretically, a two-compartment model is presented to study the thermal stresses generated during the freezing and thawing processes. The properties were measured as inputs to the model. Numerical results showed that the thermal stresses occurring in the "cryopreservation in air" process were much smaller than in the other method. The maximum thermal stress during cryopreservation occurs in the thawing process. The theoretical results could well explain published experimental results.
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